20 equilateral triangles make up the ike (icosahedron). There are 6 5fold and 10 3fold rotation axis (and further symmetry elements which are ignored in this observation). The edges of the ike can be connected by triangles (first number) and by pentagons (second number). Thus 13 polyhedra appear, which are grouped in the following way: 5 pyramidal and 1 antiprismatic polyhedra have a 5fold axis, 3 pyramidal and 2 antiprismatic figures have a 3fold axis. There are 2 figures with icosahedral symmetry, they are the great dodecahedron (gad) and the ike itself.


Ike-facetings by R. Klitzing:

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